It's well established in the Star Wars universe that all you need to create gravity is a floor. Take, for example, any scene from within any of the space ships. Gravity is never a problem.
Of course, a deep chasm also seems to create gravity, as seen in the first movie when Luke and Leia swing from one ramp to another to escape the stormtroopers chasing them.
Regardless, it's easy to see from the blueprints that the layout is stacked like your first image.
Edit: upon closer examination it turns out it's both. The plans show three 'concentric surface decks' that apparently work like your second image. So I guess the answer is 'it depends on where you are in the death star', and, I guess, which way 'down' is where you are.
Some things I've learned about the olympics from the NBC coverage in the US.
There really not much happening there most of the time. So they have to fill the time with shots of US gymnasts drinking from water bottles and sitting around in their chairs, or of US runners standing around in the hallway before the race.
I've heard rumors of other sports, but it seems the only ones that really are going on are the ones that US competitors are dominating.
The US is the best at everything. Other countries make mistakes, but US competitors are always flawless and in the front.
There is a lot of beach volleyball happening all the time.